BO using Custom GP Network model (DSVI, rsample, condition_on_observations, posterior_transform)

[saksham-kit]

I have made a custom partially observable Gaussian process network (POGPN) that uses variational inference for the posterior. The posterior is a DAG where each node has a posterior that can be MVN, MTMVN, categorical, or Bernoulli. I wrapped the MVN and MTMVN with GPyTorchPosterior and made a custom wrapper for the Categorical posterior using the Gumbel distribution. I also make sure that the optimization objective/node is continuous. I have integrated it with GPyTorch well and can use different input and output transforms from BoTorch. To be able to do BO using SAA with the POGPN model using BoTorch, I have a few questions:

rsample doubts

1. The documentation mentions that we only need to create a Posterior object with rsample. But the MCSampler uses the method rsample_with_base_samples. So, should I implement only rsample (with the base_sample argument like in previous versions) or rsample_with_base_samples differently?
2. Since I want to use batch shape for the MC acquisition, should the base samples be of the event shape for each node and expanded to the batch shape, or should they be sampled from a batch of normal distributions? I do not understand the use of base samples clearly.
3. In your understanding, can I propagate the rsamples created in the root node using base_samples through the DAG to create the posterior, or should I make base samples in each node?
4. Would it also help me use base_sample in the forward method of the model to use SAA during DSVI?

condition_on_observations

1. Do I need condition_on_observations to implement qlogEI or qEI on my POGPN model?
2. If I need to, what is its exact use?
3. Do I need to store the train_x, train_y data in the model compulsorily?

Posterior transform

1. When and how to use the posterior transform.
2. Can you give some hints on how I could integrate it with my posterior or model?

I thank you for any support possible.